A 30° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 60°.
30° is one twelfth (1/12) of a full circle, or π/6 radians. The minute hand of a clock sweeps 30° in 5 minutes. If you face north and turn 30° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
30° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 60° |
| Supplement (adds to 180°) | 150° |
| Explement (adds to 360°) | 330° |
| Radians | π/6 ≈ 0.523599 |
| Gradians | 33.3333 grad |
| Fraction of a turn | one twelfth (1/12) (8.33%) |
| Degrees, minutes, seconds | 30° 0′ 0″ |
| Slope (grade) | 57.74% |
| Roof pitch | 6.93/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 30°
| Function | Value |
|---|---|
| sin 30° | 1/2 ≈ 0.5 |
| cos 30° | √3/2 ≈ 0.866025 |
| tan 30° | √3/3 ≈ 0.57735 |
30° on a protractor
How to draw a 30° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 30° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 30°.
Drawing it a 30° angle without a protractor (compass and ruler)
- Construct a 60° angle, then bisect it.
Where you see 30° angles
- The classic 30-60-90 drafting triangle (set square) has a 30° corner.
- A hexagonal frame or planter uses 30° miter cuts.
- At 1:00 the hands of a clock are exactly 30° apart.
- A 7/12 roof pitch is 30.26°, very close to 30°.
- A board sloped at 30° rises about 69.3 inches over a 10-foot (120-inch) run.
- 30° of latitude on Earth spans roughly 2,072 miles north to south.
- The Earth turns 30° on its axis in about 2 hours.
Related angles
30° angle FAQ
What type of angle is 30°?
A 30° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 30°?
The complement of 30° is 60° (together they make 90°), and the supplement is 150° (together they make 180°).
How many radians is 30 degrees?
30° = π/6 radians ≈ 0.5236 rad. To convert degrees to radians, multiply by π/180: 30 × π/180 = π/6.
What is 30° as a slope or roof pitch?
30° is a 57.7% slope, which is a roof pitch of 6.93/12 (a rise of about 6 7/8 inches for every 12 inches of run).